Presumably, whenever it connects, it gets several items, and the software rotates them as designed. So days ago, it likely got several images, some of which are just being shown now.

Exactly right. And those images do have an expiration date embedded in them. After you haven't synced for a period of time (I forget how long, I don't have that Kindle anymore), you'll start getting a screen that says you need to sync to see new offers.